Question

Question #3f7b3

Answer 1

Percentage change in area is

`=100(1-k)^2`
where k is the ratio of reduction in width to the original width

Explanation:

I have made an attempt to express the change in area in terms of percentage change

Given:
`L=5W`
where,
`L` is the length of a rectangle
`W` is the width of a rectangle

Area of rectangle is `A=LW`
Area of rectangle `A = 5W.W`
Area of rectangle `A = 5W^2`
New width `W'=W-5`
Length becomes L'=5(W-5)
Area of new rectangle `A'=L'W'`
Area of new rectangle `A'=5(W-5)(W-5)`
Area of new rectangle `A'=5(W-5)^2`

Change in area is
`delA = A'=A`
`delA=5(W-5)^2`
Area `A = 5W^2`

Percentage change in area is
`100(delA)/A = (100 )5(W-5)^2/(5W^2`
`=100(1-k)^2`
where k is the ratio of reduction in width to the original width